Acontainer with 0.317 l of water is placed into microwave and is then radiated with electromagnetic energy that has a wavelength of 13.3 cm. the temperature of the water then rose by 74.3 °c. calculate the number of photons that were absorbed by the water. assume water has a density of 1.00 g·ml–1 and its specific heat is 4.184 j·g–1·°c–1

The number of photons absorbed by the water is

Explanation:

where,

E = energy of the photon

h = Planck's constant  =

c = speed of light  =

= wavelength of photon  = 13.3 cm = 0.133 m   (Conversion factor:  1 m = 100 cm )

Putting values in above equation, we get:

To calculate the mass of water, we use the equation:

Density of water = 1 g/mL

Volume of water = 0.317 L = 317 mL     (Conversion factor:  1 L = 1000 mL )

Putting values in above equation, we get:

where,

q = heat absorbed

m = mass of water = 317 g

c = specific heat capacity of water = 4.184 J/g°C

= change in temperature = 74.3°C

Putting values in above equation, we get:

Putting values in above equation, we get:

Hence, the number of photons absorbed by the water is

water and alcohols have similar properties because water molecules contain hydroxyl groups that can form hydrogen bonds with other water molecules and with alcohol molecules, and likewise alcohol molecules can form hydrogen bonds with other alcohol molecules as well as with water.